Statistics

Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in "acid rain."
The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0. The pH of rain at one location varies among rainy days according to a Normal distribution with mean 5.43 and standard deviation 0.54.
Exercise 3.31 (in your textbook) concerns the acidity (measured by pH) of rainfall.
A sample of 105 rainwater specimens had mean pH 5.43, standard deviation 0.54, and five-number summary 4.33, 5.05, 5.44, 5.79, 6.81.

Compare the mean and median and also the distances of the two quartiles from the median.
Does it appear that the distribution is quite symmetric? Why?
Choose the most accurate answer below, for these data:

A. The median is relatively resistant measure, while the mean isn't. Therefore the mean gets pulled further away from the direction of a long tail. Since the mean is lower than the median, we conclude that the distribution has a right-hand tail.
B. The third quartile is closer to the median than the first quartile is. This indicates that the third quartile may have been pulled up by a right-hand skew in the distribution.
C. The median is a relatively resistant measure, while the mean isn't. Therefore the mean gets pulled further in the direction of a long tail. Since the mean is smaller than the median, we conclude that the distribution has a left-hand tail.
D. The third quartile is closer to the median than the first quartile is. This indicates that the third quartile may have been pushed down by a left-hand skew in the distribution.
E. The third quartile is closer to the median than the first quartile is. This indicates that the third quartile may have been pushed down by a right-hand skew in the distribution.
F. The mean is a relatively resistant measure, while the median isn't. Therefore the median gets pulled further away from the direction of a long tail. Since the median is lower than the mean, we conclude that the distribution has a right-hand tail.
G. The data on the mean, quartiles and median provide us no indication that this distribution is skewed.

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  1. The median is a relatively resistant measure, while the mean isn't. Therefore the mean gets pulled further in the direction of a long tail. Since the mean is smaller than the median, we conclude that the distribution has a left-hand tail.

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